The invention is based on a method as described herein. Apparatuses for performing such a method are known. However, the difficulty with them is in maintaining reliable ignition capacity in an operating mixture of fuel and air for the internal combustion engine where the mixture has been made as lean as possible. This apparatus on the one hand utilizes the fuel enrichment, attained by means of an established potential vortex formation in the fresh mixture flowing into the ignition chamber, in the outer edge areas of the vortex for the purpose of increasing the ignition capacity of the relatively lean operating mixture; in addition, it also utilizes ignition within the boundary layer of this vortex flow, with a spark which leaps from an electrode over to the ignition chamber wall, which improves the ignition capacity. Furhermore, by controlling the wall temperature such that it is at a high level, good heating of the mixture to be ignited is also sought, which likewise increases its ignition capacity. This apparatus has the disadvantage, however, that ignition of the fresh mixture in the ignition chamber takes place in the rearward end of the ignition chamber so as not to place excessive thermal stress on the electrode of the spark plug. At that location, however, an increased remnant gas component from the work cycle completed earlier must be expected, which again impairs ignition capacity. Known apparatuses which have a transverse scavenging characteristic for the purpose of removing the remnant gas from the ignition chamber do not enable the sufficiently forceful establishment of the vortex, with the known advantages which that would provide, and are cooled down to a greater extent as well. The provision which can be learned from other proposals, that is, locating the ignition electrode in areas having a fresh charge which is low in remnant gas in order to increase the ignition capacity of the mixtures has the disadvantage that the electrode is exposed to excessive heat stress, especially after ignition has taken place, which soon causes wear in the electrode.